Permanent magnets are of great value in many fields of science and engineering. In particular, they find application in the field of Magnetic Resonance Imaging (MRI) and Spectroscopy (MRS). Within these latter applications it is of paramount importance that extremely high degrees of magnetic field homogeneity (of the order of one part per million) are achieved within an ROI.
In permanent magnets the distribution of the magnetic material determines how the resulting magnetic field varies over space. In both permanent magnetic and electromagnetic MRI and MRS machines, manufacturing imperfections result in unacceptable inhomogeneities. To improve the homogeneity of an existing field over an ROI it is known to place permanent magnetic materials (termed passive shims) in the magnetic field to achieve this improvement of homogeneity.
The problem of distributing magnetic material to produce, or modify an existing magnetic field is one of a class known collectively as the near field problem. In particular, it requires the determination of the distribution of material to produce a field of particular character—varying in a specific manner in space, for example a uniform field in a proximate region. The total magnetic field from a magnetic structure is a nonlinear convolution of the spatial distribution of material with the field of a magnetic dipole. While it is relatively straightforward to determine the resulting field from a given distribution of magnetic material, generally, the components of a convolution are not invertable. Consequently, determining the optimum distribution of magnetic material to produce a magnetic field of a specific type in an ROI has proven to be extremely difficult.
One known method of electromagnetic coil design is the Target field approach as disclosed in European Patent No. EP-A-0 252 634 or its US equivalent U.S. Pat. No. 4,896,129. As it is based on an assumed a priori mathematical expression for the total field, an optimum resulting field is hard to achieve.
An alternative approach is disclosed in European Patent EP-A-0601101 and its US equivalent U.S. Pat. No. 5,266,913, the content of which is hereby incorporated by reference. It is concerned with the design of shielded electromagnetic coils, and employs forward substitution and least squares minimization to optimize the field produced by electromagnets specifically within the ROI, whilst achieving a null field outside of the confines of the coil structure.
There are significant differences in the form of the magnetic fields generated by active electromagnets, and those resulting from the use of magnetic materials. Consequently, electromagnetic coil design and the design of permanent magnets involve quite separate design considerations.
The object of the present invention is to achieve an improved method of designing permanent magnetic structures.